CompSci590.03 Instructor:!Ashwin!Machanavajjhala!

Implemen'ng Differen'al Privacy & Side-‐channel a8acks

CompSci 590.03 Instructor: Ashwin Machanavajjhala

1 Lecture 17 : 590.03 Fall 13

Outline •  Differen'al Privacy Implementa'ons

–  PINQ: Privacy Integrated Queries [McSherry SIGMOD ‘09] –  Airavat: Privacy for MapReduce [Roy et al NDSS ‘10]

•  A8acks on Differen'al Privacy Implementa'ons –  Privacy budget, state and 'ming a8acks [Haeberlin et al SEC ‘11]

•  Protec'ng against a8acks –  Fuzz [Haeberlin et al SEC ‘11] –  Gupt [Mohan et al SIGMOD ‘12]

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Differen'al Privacy •  Let A and B be two databases such that B = A – {t}.

•  A mechanism M sa'sfies ε-‐differen'al privacy, if for all outputs O, and all such A, B

P(M(A) = O) ≤ eε P(M(B) = O)

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Differen'al Privacy •  Equivalently, let A and B be any two databases •  Let A Δ B = (A – B) U (B – A) … or the symmetric difference

•  A mechanism M sa'sfies ε-‐differen'al privacy, if for all outputs O,

P(M(A) = O) ≤ eε |A Δ B| P(M(B) = O)

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PINQ: Privacy Integrated Queries •  Implementa'on is based on C#’s LINQ language

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[McSherry SIGMOD ‘09]

PINQ

•  An analyst ini'ates a PINQueryable object, which in turn recursively calls other objects (either sequen'ally or in parallel).

•  A PINQAgent ensures that the privacy budget is not exceeded.

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PINQAgent: Keeps track of privacy budget

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PINQ: Composi'on

•  When a set of opera'ons O1, O2, … are performed sequen'ally, then the budget of the en're sequence is the sum of the ε for each opera'on.

•  When the opera'ons are run in parallel on disjoint subsets of the data, the privacy budget for the all the opera'ons is the max ε.

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Aggrega'on Operators

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Aggrega'on operators Laplace Mechanism •  NoisyCount •  NoisySum

Exponen1al Mechanism •  NoisyMedian •  NoisyAverage

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PINQ: Transforma'on Some'mes aggregates are computed on transforma'ons on the data •  Where: takes as input a predicate (arbitrary C# func'on), and

outputs a subset of the data sa'sfying the predicate •  Select: Maps each input record into a different record using a C#

func'on

•  GroupBy: Groups records by key values

•  Join: Takes two datasets, and key values for each and returns groups of pairs of records for each key.

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PINQ: Transforma'ons Sensi'vity can change once transforma'ons have been applied.

•  GroupBy: Removing a record from an input dataset A, can change

one group in the output T(A). Hence, |T(A) Δ T(B)| = 2 |A Δ B|

•  Hence, the implementa'on of GroupBy mul'plies ε by 2 before recursively invoking the aggrega'on opera'on on each group.

•  Join can have a much larger (unbounded) sensi'vity.

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Example

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Covert Channel •  Key assump'on in differen'al privacy implementa'ons:

The querier can only observe the result of the query, and nothing else. –  This answer is guaranteed to be differen'ally private.

•  In prac'ce: The querier can observe other effects. –  E.g, Time taken by the query to complete, power consump'on, etc. –  Suppose a system takes 1 minute to answer a query if Bob has cancer and

1 micro second otherwise, then based on query 'me the adversary may know that Bob has cancer.

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Threat Model •  Assume the adversary (querier) does not have physical access to

the machine. –  Poses queries over a network connec'on.

•  Given a query, the adversary can observe: –  Answer to their ques1on –  Time that the response arrives at their end of the connec1on –  The system’s decision to execute the query or deny (since the new query

would exceed the privacy budget)

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Timing A8ack Func'on is_f(Record r){ if(r.name = Bob && r. disease = Cancer) sleep(10 sec); // or go into infinite loop, or throw excep3on return f(r);

} Func'on counv(){ var fs = from record in data

where (is_f(record)) print fs.NoisyCount(0.1);

}

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Timing A8ack Func'on is_f(Record r){ if(r.name = Bob && r. disease = Cancer) sleep(10 sec); // or go into infinite loop, or throw excep3on return f(r);


where (is_f(record)) print fs.NoisyCount(0.1);

}

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If Bob has Cancer, then the query takes > 10 seconds If Bob does not have Cancer, then query takes less than a second.

Global Variable A8ack Boolean found = false; Func'on f(Record r){ if(found) return 1; if(r.name = Bob && r.disease = Cancer){ found = true; return 1; } else return 0;


where (f(record)) print fs.NoisyCount(0.1);

}

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Global Variable A8ack Boolean found = false; Func'on f(Record r){ if(found) return 1; if(r.name = Bob && r.disease = Cancer){ found = true; return 1; } else return 0;

} Func'on numHealthy(){ var health = from record in data

where (f(record)) print health.NoisyCount(0.1);

}

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Typically, the Where transforma1on does not change the sensi1vity of the aggregate (each record transformed into

another value). But, this transforma1on changes the sensi1vity – if Bob has

Cancer, then all subsequent records return 1.

Privacy Budget A8ack Func'on is_f(Record r){ if(r.name = Bob && r.disease = Cancer){ run a sub-‐query that uses a lot of the privacy budget; } return f(r);



}

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Privacy Budget A8ack Func'on is_f(Record r){ if(r.name = Bob && r.disease = Cancer){ run a sub-‐query that uses a lot of the privacy budget; } return f(r);



}

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If Bob does not has Cancer, then privacy budget decreases by 0.1. If Bob has Cancer, then privacy budget decreases by 0.1 + Δ.

Even if adversary can’t query for the budget, he can detect the change in budget by coun1ng how many more queries are

allowed.





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Fuzz: System for avoiding covert-‐channel a8acks

•  Global variables are not supported in this language, thus ruling our state aFacks.

•  Type checker rules out budget-‐based channels by sta'cally checking the sensi'vity of a query before they are executed

•  Predictable query processor ensures that each microquery takes the same amount of 'me, ruling out Jming aFacks.

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Fuzz Type Checker

•  A primi've is cri'cal if it takes db as an input.

•  Only four cri'cal primi'ves are allowed in the language –  No other code is allowed.

•  A type system that can infer an upper bound on the sensi'vity of any program (wri8en using the above cri'cal primi'ves). [Reed et al ICFP ‘10]

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Handling 'ming a8acks •  Each microquery takes exactly the same 'me T

•  If it takes less 'me – delay the query

•  If it takes more 'me – abort the query –  But this can leak informa1on! –  Wrong Solu1on

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Handling 'ming a8acks •  Each microquery takes exactly the same 'me T

•  If it takes less 'me – delay the query

•  If it takes more 'me – return a default value

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Fuzz Predictable Transac'on •  P-‐TRANS (λ, a, T, d)

–  λ : func'on –  a : set of arguments –  T : Timeout –  d : default value

•  Implemen'ng P-‐TRANS (λ, a, T, d) requires:

–  Isola'on: Func'on λ(a) can be aborted without wai'ng for any other func'on

–  Preemptability: λ(a) can be aborted in bounded 'me –  Bounded Dealloca'on: There is a bounded 'me needed to deallocate

resources associated with λ(a)

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GUPT

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GUPT: Sample & Aggregate Framework

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Sample and Aggregate Framework

–  S = range of the output –  L = number of blocks

Recall from previous lecture: Theorem [Smith STOC ‘09]: Suppose database records are drawn i.i.d. from

some probability distribu'on P, and the es'mator (func'on f) is asympto'cally normal at P. Then if L = o(√n), then the average output by the Sample Aggregate framework converges to the true answer to f.

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Es'ma'ng the noise •  Sensi'vity of the aggrega'on

func'on = S/L –  S = range of the output –  L = number of blocks

•  Sensi'vity is independent of the actual program f

•  Therefore, GUPT avoids a>acks using privacy budget as the covert channel.

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Es'ma'ng the noise

•  Sensi'vity of the aggrega'on func'on = S/L –  S = range of the output –  L = number of blocks

•  Output range can be : –  Specified by analyst, or –  αth and (100 -‐ α)th percen'les can be es'mated using Exponen'al

Mechanism, and a Windsorized mean can be used as the aggrega'on func'on.

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Handling Global State a8acks •  The func'on is computed on each block in an isolated execuJon

environment.

–  Analyst sees only the final output, and cannot see any intermediate output or sta'c variables.

–  Global variables can’t inflate the sensi'vity of the computa'on (like in the example we saw) … because the sensi'vity only depends on S and L and not on the func'on itself.

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Handling Timing A8acks Same is in Fuzz … •  Fix some es'mate T on the maximum 'me allowed for any

computa'on (on a block) •  If computa'on finishes earlier, then wait 'll 'me T elapses •  If computa'on takes more 'me, stop and return a default value.

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Comparing the two systems GUPT

•  Allows arbitrary computa'on. But, accuracy is guaranteed for certain es'mators.

•  Privacy-‐budget aFack: Sensi'vity is controlled by S (output range) and L (number of blocks) that are sta'cally es'mated

•  State aFack: Adversary can’t see any sta'c variables.

•  Timing aFack: Time taken across all blocks is predetermined.

FUZZ

•  Allows only certain cri'cal opera'ons.

•  Privacy-‐budget aFack: Sensi'vity is sta'cally computed.

•  State aFack: Global variables are disallowed

•  Timing AFack: Time taken across all records is predetermines

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Summary •  PINQ (and Airavat) are frameworks for differen'al privacy that

allow any programmer to incorporate privacy without needing to know how to do Laplace or Exponen'al mechanism.

•  Implementa'on can disclose informa'on through side-‐channels –  Timings, Privacy-‐budget and State a8acks

•  Fuzz and GUPT are frameworks that disallow these a8acks by –  Ensuring each query takes a bounded 'me on all records or blocks –  Sensi'vity is sta'cally es'mated (rather than dynamically) –  Global sta'c variables are either inaccessible to adversary or disallowed

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Open Ques'ons •  Are these the only a8acks that can be launched against a differen'al

privacy implementa'on?

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Least significant bits and Laplace Mechanism

•  Suppose laplace mechanism is implemented using standard floa'ng point,

•  Certain outputs are more likely than others

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[Mironov CCS ‘12]



•  Certain outputs may not appear

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[Mironov CCS ‘12]



•  Both can happen simultaneously

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[Mironov CCS ‘12]


•  Sensi'vity computa'on under floa'ng point is also tricky (assume le~ to right summa'on in the following example):

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[Mironov CCS ‘12]

Open Ques'ons •  Are these the only a8acks that can be launched against a differen'al

privacy implementa'on? –  No. Laplace mechanism can leak informa'on when implemented using standard

floa'ng point arithme'c

•  Current implementa'ons only simple algorithms for introducing privacy – Laplace and Exponen'al mechanisms. Op'mizing error for batches of queries and advanced techniques (e.g., sparse vector) are not implemented. Can these lead to other a8acks?

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References F. McSherry, “PINQ: Privacy Integrated Queries”, SIGMOD 2009 I. Roy, S. Se8y, A. Kilzer, V. Shma'kov, E. Witchel, “Airavat: Security and Privacy for

MapReduce”, NDSS 2010 A. Haeberlin, B. Pierce, A. Narayan, “Differen'al Privacy Under Fire”, SEC 2011 J. Reed, B. Pierce, M. Gaboardi, “Distance makes types grow stronger: A calculus for

differen'al privacy”, ICFP 2010 P. Mohan, A. Thakurta, E. Shi, D. Song, D. Culler, “Gupt: Privacy Preserving Data Analysis

Made Easy”, SIGMOD 2012 A. Smith, "Privacy-‐preserving sta's'cal es'ma'on with op'mal convergence rates", STOC

2011 I. Mironov, “On significance of the least significant bits for differen'al privacy ppt”, CCS

2012

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CompSci590.03 Instructor:!Ashwin!Machanavajjhala!